MathDB
2017 A10: A Surprising Polynomial FE

Source:

January 29, 2017
algebrapolynomial

Problem Statement

Let cc denote the largest possible real number such that there exists a nonconstant polynomial PP with P(z2)=P(z−c)P(z+c)P(z^2)=P(z-c)P(z+c) for all zz. Compute the sum of all values of P(13)P(\tfrac13) over all nonconstant polynomials PP satisfying the above constraint for this cc.
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